The pictures work. First time that I see a fusible link in that location in the engine bay. But the colour the green wire is strange, normally a fusible link wire is red colour. Also the blue thick wire there seems to be not original (?). Maybe it was installed later not by BMW. Try to find out where they go from ....to
Is the battery located under rear seat passenger side or in engine bay? Both was possible on E34.

My battery is in the engine bay. I also tried looking for the fusible link under the rear seat where the battery would be located but could not find anything.
You are correct, the blue wire was installed by my dad and me. It connects two wires that were used by the workshop where the car was (without success) being diagnosed after getting towed from my house be the ADAC (German Drivers Club).
The mechanics at the workshop used the wires to bypass the starter in order to test if it was still working.
My dad and me connected these two wires and installed a button switch which could be used to bypass the starter on demand.
Why did we committ such a weird act of Frankenstein-experiments, you may wonder. Well, the answer is simple: Before we found out that the car starts fine after pulling the GM, we were looking for an improvised way to get it running. And a switch is much nicer than bypassing the two wires with an additional wire. I'm 100% sure that this little "feature" is not messing with the car. All problems were there before and nothing changed after we did install the switch.

o.k., battery in engine bay, that is important for us. As a general rule we can say the fusible link is always close to the battery. Looks like it is a 50A fusible link.
Here - that is again a US 525 - they show that that fusible link is 80A http://www.bmwe34.net/E34main/Mainte...sible_link.htm
the failure syndromes they mention there = Failure syndromes: Intermittent simultaneous failure of wipers, sunroof, windows, central locking, radio, No power, like if the battery was dead = that is mainlyl GM related = Zentrale Karrosserie Elektronik.
It may be that your 518 has only one fusible link.

my car broke down on my way to work tonight. Here's what happened. I was driving around 50km/h when I noticed that my gas pedal was very sluggish (Schwergängig, not sure of correct translation).
So I pressed it down with a bit more force. It suddenly gave in and my engine fired up to 6000rpm even when I let my foot of the pedal.
Panic-stricken I came to a halt and turned off the engine.
I then removed the cover of the bowden-cable over the intake and tried to examine it.The bowden cable was very loose and flaccid. Since the cable is held in place inside some kind of plastic-screw, I tried screwing it back in a little, so it would be tightened again.
I started the engine again but it immediatly fired up to max rpm again, so I quickly turned it off. The cable is NOT broken, however. I can press down the pedal and the throttle valve moves.
I then called the Auto-Club and got the car towed to the a workshop nearby.
I read a bit on the internet and learned that this could be caused by a broken or dirty throttle valve. I'll go to the workshop tomorrow morning, right after completing my nightshift at work. Does anyone have an idea what might have caused this?
Hell, this was scary, especially since the engine was completely cold. I hope that the 5 seconds of max rpm didn't damage anything.

the high-rev-issue was fixed easily. It was just a dirty throttle valve that got stuck. After spraying it with brake cleaner, everything is now fine again.
Today I installed two more GMs. Unfortunately it brought no change at all.
I'm gonna focus now on finding that damned 50a fusible link.
I will also revisit the wiring loom under that carpet on the left side of the car. I'm sure the culprit must sit there.
I'll keep you updated about any results.

I did it! The BMW is running great again!
The culprit was a 50a fusible link under the rear seat in a small black box. It appears as I have one rare BMW that has two black boxes for the fusible links and no fuses under heatshrink.

I did it! The BMW is running great again!
The culprit was a 50a fusible link under the rear seat in a small black box. It appears as I have one rare BMW that has two black boxes for the fusible links and no fuses under heatshrink.

Thank you to everyone who helped me.

Until then,

Best regards from Germany!

That's really great news. Well done for sticking in there FTW! These problems can be so frustrating, but now you can enjoy your new life with the old-school e34

So 518i has its body electronics 50A link under the rear seat, before it feeds the main body distribution box back there? Interesting, but in a black box you say? Or is it a cover that opens to allow you to change the fuse? Where? Near the power distribution box LHS, or the open area where the battery normally is on 6 and 8 cylinder models?

The 80A one under your windshield had us wondering, it looked factory to me and for a car with the battery under the hood, that'd have been good enough for the 'loom' wizards in the 90s. These days the looms are all made by robot, not hand-bound with PVC and fabric tape like BMW had been doing since WWII until it introduced the e39 which was designed with Computer Area Networking (CAN).

Again, great work, and thanks for keeping us up to date on your troubles!